!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-permutation-symmetry !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check whether a model is invariant with respect to atom permutations that preserve species, i.e. swapping any two atoms with the same species must not change the energy or forces. This must be true for all models. The check is performed for a randomly distorted non-periodic diamond cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. The energy and forces of each configuration are compared with one where each atom is randomly swapped with another atom of the same species. The energy and forces must remain unchanged. The verification check will pass if these conditions are satisfied for all configurations that the model is able to compute. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_MEAM_MaiselKoZhang_2017_VNiTi__SM_971529344487_000 Supported species : Ni Ti V random seed = 13 lattice constant (orig) = 5.000 perturbation amplitude = 0.500 number unit cells per side = 2 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ni (Configuration in file "config-Ni.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [13, 62, 7, 10, 14, 9, 31, 2, 22, 5, 3, 20, 49, 0, 4, 17, 28, 15, 44, 58, 11, 48, 8, 52, 51, 55, 57, 33, 16, 30, 29, 6, 47, 27, 45, 46, 59, 39, 56, 37, 50, 53, 43, 42, 18, 34, 35, 32, 21, 12, 40, 24, 23, 41, 60, 25, 38, 26, 19, 36, 54, 63, 1, 61] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -22.167028805 V(r_1,...,r_N) = -22.167028805 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -1.48476912e+00 -1.04639753e+00 -1.27685785e+00 | -1.48476912e+00 -1.04639753e+00 -1.27685785e+00 1 -6.49414133e+00 -1.73661762e+01 1.23454511e+01 | -6.49414133e+00 -1.73661762e+01 1.23454511e+01 2 -4.67084173e-01 6.50707802e+00 -2.10714017e+01 | -4.67084173e-01 6.50707802e+00 -2.10714017e+01 3 8.04807928e+00 1.16796844e+01 9.29422150e+00 | 8.04807928e+00 1.16796844e+01 9.29422150e+00 4 -1.33743787e+00 2.98303962e-01 6.64273126e-01 | -1.33743787e+00 2.98303962e-01 6.64273126e-01 5 3.67357825e-01 -1.48367097e+01 5.51249071e+00 | 3.67357825e-01 -1.48367097e+01 5.51249071e+00 6 -6.63788767e-01 -3.64272627e-01 -4.59291962e-01 | -6.63788767e-01 -3.64272627e-01 -4.59291962e-01 7 -1.52486879e+01 4.51438157e+01 -2.93670779e+01 | -1.52486879e+01 4.51438157e+01 -2.93670779e+01 8 -1.73253792e+00 4.24390801e-01 -1.29709296e+00 | -1.73253792e+00 4.24390801e-01 -1.29709296e+00 9 7.17164518e-01 1.97585763e+00 9.94231585e-01 | 7.17164518e-01 1.97585763e+00 9.94231585e-01 10 -5.53315148e-01 8.70834074e-03 7.12420564e-01 | -5.53315148e-01 8.70834074e-03 7.12420564e-01 11 3.14533187e+00 -6.18885369e+00 -5.20713101e+00 | 3.14533187e+00 -6.18885369e+00 -5.20713101e+00 12 -6.07145292e+00 -6.42868457e+00 -9.64725734e-01 | -6.07145292e+00 -6.42868457e+00 -9.64725734e-01 13 2.10625917e+01 -4.50925120e+00 -9.79852107e+00 | 2.10625917e+01 -4.50925120e+00 -9.79852107e+00 14 -7.19516516e+00 1.30340335e+01 -9.65162570e+00 | -7.19516516e+00 1.30340335e+01 -9.65162570e+00 15 7.23236654e+00 2.48084971e+00 3.65114801e+00 | 7.23236654e+00 2.48084971e+00 3.65114801e+00 16 -1.62582405e+00 -3.95265264e+00 -1.04597840e+00 | -1.62582405e+00 -3.95265264e+00 -1.04597840e+00 17 -3.37389316e+00 -2.86172067e+00 5.82204357e+00 | -3.37389316e+00 -2.86172067e+00 5.82204357e+00 18 5.72981813e+00 6.15093518e+00 -3.32547302e+00 | 5.72981813e+00 6.15093518e+00 -3.32547302e+00 19 -3.15173957e+01 1.85669030e+01 -2.13953024e+01 | -3.15173957e+01 1.85669030e+01 -2.13953024e+01 20 -9.87448832e+00 -7.55743542e+00 -8.29170674e+00 | -9.87448832e+00 -7.55743542e+00 -8.29170674e+00 21 1.34916223e+01 8.79174189e+00 7.31573906e+00 | 1.34916223e+01 8.79174189e+00 7.31573906e+00 22 -3.76152029e+00 -2.17833403e+00 -7.31789613e+00 | -3.76152029e+00 -2.17833403e+00 -7.31789613e+00 23 2.69007310e+00 4.33638783e+00 4.73580006e+00 | 2.69007310e+00 4.33638783e+00 4.73580006e+00 24 -6.69705609e+00 -3.64991082e+00 -8.45256029e+00 | -6.69705609e+00 -3.64991082e+00 -8.45256029e+00 25 -2.87371703e+00 1.53978750e+01 8.65228457e-01 | -2.87371703e+00 1.53978750e+01 8.65228457e-01 26 -3.55894011e-01 -1.21564994e+00 9.14662558e-01 | -3.55894011e-01 -1.21564994e+00 9.14662558e-01 27 -1.12631692e+00 -7.75652556e-01 5.85275174e-01 | -1.12631692e+00 -7.75652556e-01 5.85275174e-01 28 3.55449273e+00 -6.93696630e+00 1.11721508e+01 | 3.55449273e+00 -6.93696630e+00 1.11721508e+01 29 2.02302819e+00 2.21402407e+00 2.75541290e+00 | 2.02302819e+00 2.21402407e+00 2.75541290e+00 30 3.05591975e+01 -1.85135324e+01 2.00342066e+01 | 3.05591975e+01 -1.85135324e+01 2.00342066e+01 31 -1.75682511e+01 1.29832438e+00 -9.29610339e+00 | -1.75682511e+01 1.29832438e+00 -9.29610339e+00 32 -3.20221150e+01 -2.80456962e+01 -2.09988132e+01 | -3.20221150e+01 -2.80456962e+01 -2.09988132e+01 33 3.22453280e+01 2.87635928e+01 1.96797263e+01 | 3.22453280e+01 2.87635928e+01 1.96797263e+01 34 2.03565487e+01 -4.93406674e+01 2.76739063e+01 | 2.03565487e+01 -4.93406674e+01 2.76739063e+01 35 -3.14623897e+00 -5.89124972e+00 1.45522997e+00 | -3.14623897e+00 -5.89124972e+00 1.45522997e+00 36 1.43130621e+00 4.71524883e-01 7.02941640e-01 | 1.43130621e+00 4.71524883e-01 7.02941640e-01 37 -2.19461987e+00 -2.11546877e+00 7.73298926e-01 | -2.19461987e+00 -2.11546877e+00 7.73298926e-01 38 -5.16904814e+01 -4.15726307e+01 -4.58747733e+01 | -5.16904814e+01 -4.15726307e+01 -4.58747733e+01 39 4.05375471e+01 3.11311360e+01 5.13447206e+01 | 4.05375471e+01 3.11311360e+01 5.13447206e+01 40 -2.72848830e+00 -1.74971229e-01 5.07097705e-01 | -2.72848830e+00 -1.74971229e-01 5.07097705e-01 41 -1.19705171e+01 2.53343732e+01 -1.46054865e+01 | -1.19705171e+01 2.53343732e+01 -1.46054865e+01 42 -1.84981819e+01 5.49251142e+00 6.39244382e+00 | -1.84981819e+01 5.49251142e+00 6.39244382e+00 43 4.62997602e+00 3.75415152e+00 4.55574692e+00 | 4.62997602e+00 3.75415152e+00 4.55574692e+00 44 1.56666667e+01 -2.60202322e+01 1.29436931e+01 | 1.56666667e+01 -2.60202322e+01 1.29436931e+01 45 -2.57918425e-01 1.03762466e+00 2.97302906e-01 | -2.57918425e-01 1.03762466e+00 2.97302906e-01 46 2.31465896e-01 1.89210229e+00 -1.10446898e+00 | 2.31465896e-01 1.89210229e+00 -1.10446898e+00 47 2.01079181e+00 -1.06778414e+00 -8.95072480e-01 | 2.01079181e+00 -1.06778414e+00 -8.95072480e-01 48 -5.32271398e+00 2.67046278e+00 3.87228724e+00 | -5.32271398e+00 2.67046278e+00 3.87228724e+00 49 2.57882278e+00 -5.29471724e+00 -4.51100959e+00 | 2.57882278e+00 -5.29471724e+00 -4.51100959e+00 50 -3.25317128e+00 -1.03808396e+01 -8.17703529e+00 | -3.25317128e+00 -1.03808396e+01 -8.17703529e+00 51 6.72251827e+00 8.61609717e+00 8.78038458e+00 | 6.72251827e+00 8.61609717e+00 8.78038458e+00 52 1.18846158e+01 1.08805061e+01 -6.73805923e+00 | 1.18846158e+01 1.08805061e+01 -6.73805923e+00 53 -1.81986695e+00 1.67030808e+00 -5.56942125e-01 | -1.81986695e+00 1.67030808e+00 -5.56942125e-01 54 -9.68656463e+00 -3.37979270e-01 -1.05775168e-02 | -9.68656463e+00 -3.37979270e-01 -1.05775168e-02 55 6.64329451e+00 4.18649780e+00 5.76970412e+00 | 6.64329451e+00 4.18649780e+00 5.76970412e+00 56 -9.38612868e+00 -8.88483538e+00 -4.11912913e+00 | -9.38612868e+00 -8.88483538e+00 -4.11912913e+00 57 2.62044869e+01 -1.01475481e+01 -2.57631974e+01 | 2.62044869e+01 -1.01475481e+01 -2.57631974e+01 58 1.82183326e+01 -2.73811257e+00 1.06055115e+01 | 1.82183326e+01 -2.73811257e+00 1.06055115e+01 59 -1.21351582e+00 -7.62225198e-01 2.19429146e-01 | -1.21351582e+00 -7.62225198e-01 2.19429146e-01 60 -1.30417085e+00 1.45265195e+00 3.53909581e-01 | -1.30417085e+00 1.45265195e+00 3.53909581e-01 61 -8.21754939e-01 1.10003954e+00 4.20742194e-01 | -8.21754939e-01 1.10003954e+00 4.20742194e-01 62 -1.32622297e+01 2.53038005e+01 2.86987303e+01 | -1.32622297e+01 2.53038005e+01 2.86987303e+01 63 6.18589791e-01 -9.09136304e-01 -8.48251559e-01 | 6.18589791e-01 -9.09136304e-01 -8.48251559e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = Ti (Configuration in file "config-Ti.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [55, 8, 57, 10, 17, 26, 16, 13, 1, 45, 3, 33, 23, 7, 40, 21, 6, 4, 49, 62, 39, 15, 38, 12, 37, 41, 5, 43, 32, 42, 54, 50, 28, 11, 35, 34, 46, 24, 22, 20, 14, 25, 29, 27, 61, 9, 36, 52, 60, 18, 31, 58, 47, 59, 30, 0, 63, 2, 51, 53, 48, 44, 19, 56] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 20.4006438599 V(r_1,...,r_N) = 20.4006438599 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -1.79492189e+00 -3.84750740e-01 -6.70329129e-01 | -1.79492189e+00 -3.84750740e-01 -6.70329129e-01 1 9.80078765e-01 2.16004835e+00 -3.28657604e+00 | 9.80078765e-01 2.16004835e+00 -3.28657604e+00 2 -6.48618473e+00 -2.21118911e+00 -3.96693882e+00 | -6.48618473e+00 -2.21118911e+00 -3.96693882e+00 3 4.26779295e+00 6.22788874e+00 7.16138835e+00 | 4.26779295e+00 6.22788874e+00 7.16138835e+00 4 1.39223562e+00 -7.18918867e+00 6.12602661e+00 | 1.39223562e+00 -7.18918867e+00 6.12602661e+00 5 -4.06029891e+00 2.58365686e+00 -1.34814087e+00 | -4.06029891e+00 2.58365686e+00 -1.34814087e+00 6 -1.14296510e+01 -9.76902234e+00 -8.19404911e+00 | -1.14296510e+01 -9.76902234e+00 -8.19404911e+00 7 6.61084684e+00 4.94402413e+00 3.63918283e+00 | 6.61084684e+00 4.94402413e+00 3.63918283e+00 8 -1.11495133e+00 -1.65356183e+00 -1.10489847e+00 | -1.11495133e+00 -1.65356183e+00 -1.10489847e+00 9 1.74474257e-01 1.59329534e+00 2.84453260e+00 | 1.74474257e-01 1.59329534e+00 2.84453260e+00 10 7.97308981e-02 -1.38323214e+00 -3.07488690e+00 | 7.97308981e-02 -1.38323214e+00 -3.07488690e+00 11 2.39830025e+00 -5.82438512e-01 -1.85818426e+00 | 2.39830025e+00 -5.82438512e-01 -1.85818426e+00 12 -1.62102310e+00 -3.17463283e-01 -1.17174779e+00 | -1.62102310e+00 -3.17463283e-01 -1.17174779e+00 13 1.25058783e+00 2.04785478e+00 -1.26775450e+00 | 1.25058783e+00 2.04785478e+00 -1.26775450e+00 14 -3.00656764e+00 1.19491248e+00 -1.38518617e+00 | -3.00656764e+00 1.19491248e+00 -1.38518617e+00 15 8.62725220e+00 -2.82924559e+00 1.42296162e+00 | 8.62725220e+00 -2.82924559e+00 1.42296162e+00 16 -9.45287666e+00 -1.44488984e+01 -1.32273574e+00 | -9.45287666e+00 -1.44488984e+01 -1.32273574e+00 17 3.75139810e+00 4.44382261e+00 5.38737025e+00 | 3.75139810e+00 4.44382261e+00 5.38737025e+00 18 5.43672720e+00 9.33641198e+00 -6.38865308e+00 | 5.43672720e+00 9.33641198e+00 -6.38865308e+00 19 -8.09822289e+00 2.24492580e+00 -4.27371025e+00 | -8.09822289e+00 2.24492580e+00 -4.27371025e+00 20 -6.46643406e+00 -2.25460645e+00 -3.52331659e+00 | -6.46643406e+00 -2.25460645e+00 -3.52331659e+00 21 8.30566359e+00 5.57926465e+00 8.34345834e+00 | 8.30566359e+00 5.57926465e+00 8.34345834e+00 22 -2.52145127e+00 -5.44743214e+00 -2.54281764e+00 | -2.52145127e+00 -5.44743214e+00 -2.54281764e+00 23 2.86191342e+00 6.94077337e+00 1.80510767e+00 | 2.86191342e+00 6.94077337e+00 1.80510767e+00 24 7.03240714e+00 1.46256074e+00 -3.38726604e+00 | 7.03240714e+00 1.46256074e+00 -3.38726604e+00 25 -2.90337662e+00 -9.03166759e+00 5.76850654e+00 | -2.90337662e+00 -9.03166759e+00 5.76850654e+00 26 -2.28868023e+00 2.70472331e+00 -1.24858324e+01 | -2.28868023e+00 2.70472331e+00 -1.24858324e+01 27 3.36907958e+00 3.38092277e+00 4.30119592e+00 | 3.36907958e+00 3.38092277e+00 4.30119592e+00 28 1.44812583e+00 -7.39193535e+00 -8.32923316e+00 | 1.44812583e+00 -7.39193535e+00 -8.32923316e+00 29 4.04558951e+00 7.57462456e+00 8.09735140e+00 | 4.04558951e+00 7.57462456e+00 8.09735140e+00 30 6.52358139e+00 -1.13565982e+01 -1.25458378e+00 | 6.52358139e+00 -1.13565982e+01 -1.25458378e+00 31 -2.65618454e+00 1.19828401e+01 9.50473725e+00 | -2.65618454e+00 1.19828401e+01 9.50473725e+00 32 2.13209868e-01 -8.74058994e-01 -3.22396006e+00 | 2.13209868e-01 -8.74058994e-01 -3.22396006e+00 33 1.27133009e+00 2.99883032e+00 3.90119204e-01 | 1.27133009e+00 2.99883032e+00 3.90119204e-01 34 2.00436385e+00 6.24886104e-01 5.87904775e+00 | 2.00436385e+00 6.24886104e-01 5.87904775e+00 35 -6.92303557e-01 -4.52949141e+00 4.01244214e-01 | -6.92303557e-01 -4.52949141e+00 4.01244214e-01 36 6.91102718e-01 -7.56651728e+00 -1.86621869e+00 | 6.91102718e-01 -7.56651728e+00 -1.86621869e+00 37 -1.34145503e+01 6.20035096e-01 1.09383503e+01 | -1.34145503e+01 6.20035096e-01 1.09383503e+01 38 -1.00914730e+01 -6.28472130e-01 -8.19782260e+00 | -1.00914730e+01 -6.28472130e-01 -8.19782260e+00 39 9.69292013e+00 3.64043635e+00 7.61679223e+00 | 9.69292013e+00 3.64043635e+00 7.61679223e+00 40 -9.42890554e-01 -1.70557285e+00 -8.52353356e-01 | -9.42890554e-01 -1.70557285e+00 -8.52353356e-01 41 -7.55550790e+00 1.10875831e+01 -1.43618668e+01 | -7.55550790e+00 1.10875831e+01 -1.43618668e+01 42 7.39894493e-01 -4.14114324e+00 1.61602258e+00 | 7.39894493e-01 -4.14114324e+00 1.61602258e+00 43 2.13707623e+01 -2.74813811e+01 -6.88868076e+00 | 2.13707623e+01 -2.74813811e+01 -6.88868076e+00 44 1.74682340e+00 -2.33941221e+01 1.29321836e+01 | 1.74682340e+00 -2.33941221e+01 1.29321836e+01 45 7.46851679e+00 1.01239321e+01 4.85432214e+00 | 7.46851679e+00 1.01239321e+01 4.85432214e+00 46 1.24930200e+01 7.72211899e+00 -9.50994537e+00 | 1.24930200e+01 7.72211899e+00 -9.50994537e+00 47 -5.05234558e+00 -2.70595640e+00 3.10431502e+00 | -5.05234558e+00 -2.70595640e+00 3.10431502e+00 48 -2.04339851e+00 -6.46798735e-01 -2.98292827e+00 | -2.04339851e+00 -6.46798735e-01 -2.98292827e+00 49 -1.31247482e+01 9.32060118e+00 -1.41329653e+01 | -1.31247482e+01 9.32060118e+00 -1.41329653e+01 50 -1.29653529e+01 -7.93378397e+00 -7.92148454e+00 | -1.29653529e+01 -7.93378397e+00 -7.92148454e+00 51 1.11015741e+01 6.96193538e+00 5.75399647e+00 | 1.11015741e+01 6.96193538e+00 5.75399647e+00 52 8.63341112e-01 -1.11241299e+01 7.55371683e+00 | 8.63341112e-01 -1.11241299e+01 7.55371683e+00 53 1.22227245e+01 2.65387799e-01 1.46970801e+01 | 1.22227245e+01 2.65387799e-01 1.46970801e+01 54 -2.61984354e+01 -2.51125313e+01 -5.20484152e+00 | -2.61984354e+01 -2.51125313e+01 -5.20484152e+00 55 2.78819255e+01 2.38369915e+01 3.99274076e+00 | 2.78819255e+01 2.38369915e+01 3.99274076e+00 56 -7.90072886e+00 8.80764609e+00 -1.45145668e+00 | -7.90072886e+00 8.80764609e+00 -1.45145668e+00 57 9.04257298e+00 -9.11387485e+00 -1.13267876e+01 | 9.04257298e+00 -9.11387485e+00 -1.13267876e+01 58 -8.62417260e+00 -3.36239286e+00 -8.95174376e+00 | -8.62417260e+00 -3.36239286e+00 -8.95174376e+00 59 7.49440899e+00 1.15790358e+00 9.63370003e+00 | 7.49440899e+00 1.15790358e+00 9.63370003e+00 60 -1.85094145e+01 2.78423836e+01 -2.19680615e+00 | -1.85094145e+01 2.78423836e+01 -2.19680615e+00 61 2.66537642e+00 4.41915506e+00 4.35968692e+00 | 2.66537642e+00 4.41915506e+00 4.35968692e+00 62 -9.45456897e+00 1.01763319e+01 1.00373165e+01 | -9.45456897e+00 1.01763319e+01 1.00373165e+01 63 2.95106323e+00 5.62748777e-01 1.74424814e+00 | 2.95106323e+00 5.62748777e-01 1.74424814e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MONOATOMIC STRUCTURE -- Species = V (Configuration in file "config-V.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [51, 33, 58, 56, 6, 19, 4, 9, 55, 7, 16, 45, 61, 46, 63, 42, 10, 31, 62, 5, 26, 40, 36, 43, 34, 60, 20, 59, 49, 41, 57, 17, 54, 1, 24, 52, 22, 39, 47, 37, 21, 29, 15, 23, 48, 11, 13, 38, 44, 28, 53, 0, 35, 50, 32, 8, 3, 30, 2, 27, 25, 12, 18, 14] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = -136.230021421 V(r_1,...,r_N) = -136.230021421 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 7.53120447e-01 4.01808048e-01 6.40515806e-01 | 7.53120447e-01 4.01808048e-01 6.40515806e-01 1 1.11222908e+00 -7.03486540e+00 -2.42085241e+00 | 1.11222908e+00 -7.03486540e+00 -2.42085241e+00 2 -6.15711131e+00 -1.49255666e+01 -6.46828750e+00 | -6.15711131e+00 -1.49255666e+01 -6.46828750e+00 3 4.39887820e+00 1.53327451e+01 4.96059787e+00 | 4.39887820e+00 1.53327451e+01 4.96059787e+00 4 4.20910505e-01 -2.35333699e-01 -3.59023553e-01 | 4.20910505e-01 -2.35333699e-01 -3.59023553e-01 5 -9.09800619e+00 5.63154815e+00 -1.53746485e+01 | -9.09800619e+00 5.63154815e+00 -1.53746485e+01 6 -5.51259793e+00 3.20402300e+00 -3.08024289e+00 | -5.51259793e+00 3.20402300e+00 -3.08024289e+00 7 1.30865138e+00 1.46382666e+00 4.11242265e+00 | 1.30865138e+00 1.46382666e+00 4.11242265e+00 8 -6.24278006e-01 5.64937014e-01 -3.20508008e-01 | -6.24278006e-01 5.64937014e-01 -3.20508008e-01 9 -9.69432596e-01 -3.68062348e-01 1.24356252e+00 | -9.69432596e-01 -3.68062348e-01 1.24356252e+00 10 1.82763978e+00 1.12006498e+00 -2.10639314e+00 | 1.82763978e+00 1.12006498e+00 -2.10639314e+00 11 -7.61247049e-01 -4.72293620e-01 1.69516023e-01 | -7.61247049e-01 -4.72293620e-01 1.69516023e-01 12 7.75856933e-01 -4.22399881e+00 -1.24997969e+00 | 7.75856933e-01 -4.22399881e+00 -1.24997969e+00 13 3.91911688e+00 5.04710198e-01 7.92164072e-01 | 3.91911688e+00 5.04710198e-01 7.92164072e-01 14 -4.16527516e+00 1.83336331e+00 1.64978004e+00 | -4.16527516e+00 1.83336331e+00 1.64978004e+00 15 -3.47317434e+00 -1.56404006e+00 1.39838791e+00 | -3.47317434e+00 -1.56404006e+00 1.39838791e+00 16 1.71083562e+00 5.04190535e-01 1.39835997e+00 | 1.71083562e+00 5.04190535e-01 1.39835997e+00 17 -1.21500831e+01 -5.14342339e+00 5.26712906e+00 | -1.21500831e+01 -5.14342339e+00 5.26712906e+00 18 1.22554484e+01 3.91194358e+00 -5.93511644e+00 | 1.22554484e+01 3.91194358e+00 -5.93511644e+00 19 -2.20875640e+00 7.79036888e-01 -6.42293499e-01 | -2.20875640e+00 7.79036888e-01 -6.42293499e-01 20 -6.59523943e-01 7.98299364e-01 -1.44559723e+00 | -6.59523943e-01 7.98299364e-01 -1.44559723e+00 21 -1.19410934e-01 -4.19988568e-01 5.75065402e-01 | -1.19410934e-01 -4.19988568e-01 5.75065402e-01 22 1.46044864e+00 -7.20214485e-01 1.04132881e+00 | 1.46044864e+00 -7.20214485e-01 1.04132881e+00 23 -1.95073718e-01 3.73181408e-02 2.91157166e-01 | -1.95073718e-01 3.73181408e-02 2.91157166e-01 24 -2.83048104e-01 2.19626102e-01 -8.85984042e-02 | -2.83048104e-01 2.19626102e-01 -8.85984042e-02 25 -7.95809939e-01 5.40472765e-01 -3.01180596e+00 | -7.95809939e-01 5.40472765e-01 -3.01180596e+00 26 1.04656591e+00 1.95169576e+00 3.15578467e+00 | 1.04656591e+00 1.95169576e+00 3.15578467e+00 27 -2.36307241e+00 -3.49459825e+00 -1.50027426e+00 | -2.36307241e+00 -3.49459825e+00 -1.50027426e+00 28 3.90324033e+00 -5.78503744e+00 -1.96071871e+00 | 3.90324033e+00 -5.78503744e+00 -1.96071871e+00 29 2.50408462e+00 2.99573794e+00 2.07489026e+00 | 2.50408462e+00 2.99573794e+00 2.07489026e+00 30 -5.34407403e-01 1.84830313e+00 3.24770875e+00 | -5.34407403e-01 1.84830313e+00 3.24770875e+00 31 -7.43795656e-01 -1.60504543e-01 2.91973954e-01 | -7.43795656e-01 -1.60504543e-01 2.91973954e-01 32 2.21174227e+00 1.81822433e+00 -4.97971338e-01 | 2.21174227e+00 1.81822433e+00 -4.97971338e-01 33 4.00933999e+00 -1.39449976e+00 -2.22446191e+00 | 4.00933999e+00 -1.39449976e+00 -2.22446191e+00 34 2.20659986e-01 2.51185837e+00 -3.07137234e-01 | 2.20659986e-01 2.51185837e+00 -3.07137234e-01 35 3.92751124e-01 7.94345074e-02 -1.96381252e-01 | 3.92751124e-01 7.94345074e-02 -1.96381252e-01 36 -1.41309962e+00 -5.92786218e-01 -7.52519020e-01 | -1.41309962e+00 -5.92786218e-01 -7.52519020e-01 37 -3.95272322e+00 -7.27202563e+00 7.68012824e+00 | -3.95272322e+00 -7.27202563e+00 7.68012824e+00 38 -4.87390195e+00 2.64972451e+00 3.68079884e+00 | -4.87390195e+00 2.64972451e+00 3.68079884e+00 39 1.48757805e+00 -6.24547293e-01 -5.64762529e-01 | 1.48757805e+00 -6.24547293e-01 -5.64762529e-01 40 9.55829314e+00 -1.04568528e+01 1.18181947e+01 | 9.55829314e+00 -1.04568528e+01 1.18181947e+01 41 5.38982867e+00 -9.52582863e-01 -5.13636066e+00 | 5.38982867e+00 -9.52582863e-01 -5.13636066e+00 42 -1.09720205e+00 1.93666986e+00 1.71602307e+00 | -1.09720205e+00 1.93666986e+00 1.71602307e+00 43 4.65635421e+00 -4.12815293e+00 -6.50693494e+00 | 4.65635421e+00 -4.12815293e+00 -6.50693494e+00 44 -2.57181836e-01 1.85268017e+00 2.42515196e-01 | -2.57181836e-01 1.85268017e+00 2.42515196e-01 45 -1.64135369e+00 1.30863953e+00 -1.89715748e+00 | -1.64135369e+00 1.30863953e+00 -1.89715748e+00 46 -5.99130529e+00 5.46294535e+00 -9.78013325e-03 | -5.99130529e+00 5.46294535e+00 -9.78013325e-03 47 8.71437052e+00 3.73964095e+00 4.22325128e+00 | 8.71437052e+00 3.73964095e+00 4.22325128e+00 48 1.09032409e+00 2.65125142e-01 1.02875096e+00 | 1.09032409e+00 2.65125142e-01 1.02875096e+00 49 5.80723572e-01 -1.99549993e+00 -2.56603435e+00 | 5.80723572e-01 -1.99549993e+00 -2.56603435e+00 50 3.40612909e-01 -1.85678379e-01 -2.85426622e+00 | 3.40612909e-01 -1.85678379e-01 -2.85426622e+00 51 6.63684348e-01 1.04671549e+00 3.34861664e+00 | 6.63684348e-01 1.04671549e+00 3.34861664e+00 52 -3.27224928e+00 1.51781576e+00 -8.93302254e-01 | -3.27224928e+00 1.51781576e+00 -8.93302254e-01 53 2.25528675e-01 -1.03148060e+00 -4.82575152e-01 | 2.25528675e-01 -1.03148060e+00 -4.82575152e-01 54 -2.07893302e+00 1.61275274e+00 -1.54701764e+00 | -2.07893302e+00 1.61275274e+00 -1.54701764e+00 55 2.46031200e+00 7.62271439e-01 2.41128825e+00 | 2.46031200e+00 7.62271439e-01 2.41128825e+00 56 -2.08789843e+00 -3.33598354e+00 -2.86836700e+00 | -2.08789843e+00 -3.33598354e+00 -2.86836700e+00 57 1.14546362e+00 2.31261225e+00 -5.50534716e-01 | 1.14546362e+00 2.31261225e+00 -5.50534716e-01 58 2.50264630e+00 -3.88781118e+00 -7.67111923e-01 | 2.50264630e+00 -3.88781118e+00 -7.67111923e-01 59 8.83148298e-01 4.80039903e+00 1.41482862e+00 | 8.83148298e-01 4.80039903e+00 1.41482862e+00 60 -2.99291650e+00 4.83647764e+00 6.97443860e+00 | -2.99291650e+00 4.83647764e+00 6.97443860e+00 61 -1.24215537e+00 -6.26936712e-01 -1.12215773e+00 | -1.24215537e+00 -6.26936712e-01 -1.12215773e+00 62 -1.97628706e+00 3.99306654e-01 2.74701234e+00 | -1.97628706e+00 3.99306654e-01 2.74701234e+00 63 -2.39077006e-01 -1.52417931e+00 -1.88701801e+00 | -2.39077006e-01 -1.52417931e+00 -1.88701801e+00 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- MIXED STRUCTURE -- Species = Ni Ti V (Configuration in file "config-NiTiV.xyz") ------------------------------------------------------------------------------------------------------------------------- Permutation list = [50, 13, 46, 41, 58, 29, 63, 43, 11, 30, 31, 8, 17, 1, 52, 59, 61, 12, 25, 20, 19, 42, 53, 27, 48, 18, 36, 23, 37, 5, 9, 10, 62, 54, 60, 56, 26, 28, 55, 51, 40, 3, 21, 7, 49, 57, 2, 47, 24, 44, 0, 39, 14, 22, 33, 38, 35, 45, 4, 15, 34, 16, 32, 6] Energy requirement: V(r_(PI 1),...,r_(PI N)) = V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). V(r_(PI 1),...,r_(PI N)) = 49.646143058 V(r_1,...,r_N) = 49.646143058 Forces requirement: f_(PI i)(r_(PI 1),...,r_(PI N)) = f_i(r_1,...,r_N), where r_i is the position of atom i, f_i is the force on atom i and PI is the permutation operator (which randomly swaps all atoms with other atoms of the same species). i f_(PI i)(r_(PI 1),...,r_(PI N)) f_i(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------- 0 -1.51909303e+01 -5.84465793e+00 -4.18374668e+00 | -1.51909303e+01 -5.84465793e+00 -4.18374668e+00 1 1.40739403e+01 7.62235845e+00 2.49010670e+00 | 1.40739403e+01 7.62235845e+00 2.49010670e+00 2 -2.77649709e+00 -9.20611804e+00 -1.82847043e+01 | -2.77649709e+00 -9.20611804e+00 -1.82847043e+01 3 2.42525998e+00 6.77606265e+00 1.91524334e+01 | 2.42525998e+00 6.77606265e+00 1.91524334e+01 4 2.78007965e-02 -1.36698288e+00 2.61719864e+00 | 2.78007965e-02 -1.36698288e+00 2.61719864e+00 5 -1.08609888e+01 -3.20596239e+00 -1.81655449e+00 | -1.08609888e+01 -3.20596239e+00 -1.81655449e+00 6 -1.23450310e+01 -1.03543056e+01 -7.93633141e+00 | -1.23450310e+01 -1.03543056e+01 -7.93633141e+00 7 -1.15229102e+01 -6.91343042e+00 1.72057280e+01 | -1.15229102e+01 -6.91343042e+00 1.72057280e+01 8 -1.71461459e-02 9.12663270e-01 -4.69700358e-02 | -1.71461459e-02 9.12663270e-01 -4.69700358e-02 9 -9.32272017e+00 1.25962670e+01 -7.08890534e+00 | -9.32272017e+00 1.25962670e+01 -7.08890534e+00 10 -3.01247654e+00 -2.33000715e+00 -6.45588155e+00 | -3.01247654e+00 -2.33000715e+00 -6.45588155e+00 11 8.87536134e+00 -5.59058846e+00 -1.74268154e+00 | 8.87536134e+00 -5.59058846e+00 -1.74268154e+00 12 9.29818764e+00 -1.11744965e+01 7.12745786e+00 | 9.29818764e+00 -1.11744965e+01 7.12745786e+00 13 -4.32317478e-01 8.12703118e-01 -1.24438374e-01 | -4.32317478e-01 8.12703118e-01 -1.24438374e-01 14 1.07992485e+01 2.71896751e+00 5.20549773e-01 | 1.07992485e+01 2.71896751e+00 5.20549773e-01 15 -1.37059215e-01 -5.28094537e+00 7.16997186e+00 | -1.37059215e-01 -5.28094537e+00 7.16997186e+00 16 -7.03149370e-02 -1.30084013e+00 -1.90988838e+00 | -7.03149370e-02 -1.30084013e+00 -1.90988838e+00 17 2.65039873e+01 -2.63130558e+01 -1.32528316e+01 | 2.65039873e+01 -2.63130558e+01 -1.32528316e+01 18 -1.02745629e-01 -2.45538458e-01 7.36280797e-01 | -1.02745629e-01 -2.45538458e-01 7.36280797e-01 19 -2.12476824e+00 1.36036753e+00 -1.24406400e+00 | -2.12476824e+00 1.36036753e+00 -1.24406400e+00 20 2.29978694e+01 1.64245035e+01 -8.87833759e+00 | 2.29978694e+01 1.64245035e+01 -8.87833759e+00 21 -9.45539389e-01 2.22125402e+00 -6.47526938e-01 | -9.45539389e-01 2.22125402e+00 -6.47526938e-01 22 -2.50051258e+01 2.67908136e+01 1.70320041e+01 | -2.50051258e+01 2.67908136e+01 1.70320041e+01 23 -9.97859139e+01 6.14441816e+01 -1.03862356e+02 | -9.97859139e+01 6.14441816e+01 -1.03862356e+02 24 -6.70247017e-01 1.36542025e+00 -1.45631335e+00 | -6.70247017e-01 1.36542025e+00 -1.45631335e+00 25 -2.42205991e+00 -4.82015271e+00 4.44713503e+00 | -2.42205991e+00 -4.82015271e+00 4.44713503e+00 26 4.66809962e+00 6.70384853e+00 -3.98159111e+00 | 4.66809962e+00 6.70384853e+00 -3.98159111e+00 27 -9.98741289e-01 -1.27116746e+00 2.14888429e-01 | -9.98741289e-01 -1.27116746e+00 2.14888429e-01 28 -4.85721734e+00 1.45355207e+01 4.63175326e+00 | -4.85721734e+00 1.45355207e+01 4.63175326e+00 29 -3.31925662e-01 1.06258929e+00 3.92604249e-01 | -3.31925662e-01 1.06258929e+00 3.92604249e-01 30 -1.47286491e+01 -1.64604740e+01 -1.77297728e+01 | -1.47286491e+01 -1.64604740e+01 -1.77297728e+01 31 1.73131830e+01 1.34230898e+01 1.93206783e+01 | 1.73131830e+01 1.34230898e+01 1.93206783e+01 32 -3.17853235e+00 6.53799734e-01 9.73894423e-01 | -3.17853235e+00 6.53799734e-01 9.73894423e-01 33 1.98229012e+01 -5.54616583e+00 -2.07310844e+00 | 1.98229012e+01 -5.54616583e+00 -2.07310844e+00 34 2.66634651e+00 1.88947407e+00 -7.64535066e+00 | 2.66634651e+00 1.88947407e+00 -7.64535066e+00 35 -3.57464285e+00 -5.83798162e+00 4.15152307e-01 | -3.57464285e+00 -5.83798162e+00 4.15152307e-01 36 -7.23483969e+00 -7.60874064e+00 -5.47733648e-01 | -7.23483969e+00 -7.60874064e+00 -5.47733648e-01 37 5.87214256e+00 2.18737513e+00 3.83212836e+00 | 5.87214256e+00 2.18737513e+00 3.83212836e+00 38 -1.68979064e+01 5.05223033e+00 9.48665262e+00 | -1.68979064e+01 5.05223033e+00 9.48665262e+00 39 2.84792117e-01 8.76402209e-01 -2.26441712e-01 | 2.84792117e-01 8.76402209e-01 -2.26441712e-01 40 -2.61056788e+00 -4.10632892e+00 -2.79133500e-01 | -2.61056788e+00 -4.10632892e+00 -2.79133500e-01 41 -8.11311035e+00 3.26141582e+00 -7.64566876e+00 | -8.11311035e+00 3.26141582e+00 -7.64566876e+00 42 1.32308379e+01 -7.15664820e-01 -3.55347668e+00 | 1.32308379e+01 -7.15664820e-01 -3.55347668e+00 43 7.38944195e-01 -4.36582523e+00 -1.30875932e+00 | 7.38944195e-01 -4.36582523e+00 -1.30875932e+00 44 -2.57727098e+00 -1.78406482e+00 -2.93179251e+00 | -2.57727098e+00 -1.78406482e+00 -2.93179251e+00 45 7.24504729e-01 3.06458630e+00 1.49545487e+00 | 7.24504729e-01 3.06458630e+00 1.49545487e+00 46 -4.33411110e-01 1.86050064e+00 1.16279291e+01 | -4.33411110e-01 1.86050064e+00 1.16279291e+01 47 3.35951344e-02 1.15649022e+00 -5.22621255e-01 | 3.35951344e-02 1.15649022e+00 -5.22621255e-01 48 -4.69436241e+00 -2.42430829e+00 -7.92487086e+00 | -4.69436241e+00 -2.42430829e+00 -7.92487086e+00 49 7.55086813e+00 1.08045610e+00 5.52992830e+00 | 7.55086813e+00 1.08045610e+00 5.52992830e+00 50 1.00334588e+02 -6.23573799e+01 1.02438902e+02 | 1.00334588e+02 -6.23573799e+01 1.02438902e+02 51 -8.77522594e+00 -4.26955529e+00 -9.63537656e+00 | -8.77522594e+00 -4.26955529e+00 -9.63537656e+00 52 -5.04498554e+00 2.23745137e-01 1.93656718e+00 | -5.04498554e+00 2.23745137e-01 1.93656718e+00 53 -7.19254601e+00 -4.89564371e+00 1.44069459e+01 | -7.19254601e+00 -4.89564371e+00 1.44069459e+01 54 -2.40917162e+01 -4.00820179e+01 -4.04426204e+01 | -2.40917162e+01 -4.00820179e+01 -4.04426204e+01 55 2.48152710e+01 3.97401034e+01 3.99127864e+01 | 2.48152710e+01 3.97401034e+01 3.99127864e+01 56 -7.49684650e+00 1.11995842e+01 -9.38109865e+00 | -7.49684650e+00 1.11995842e+01 -9.38109865e+00 57 5.35846996e+01 -3.25042457e+01 -2.07994772e+01 | 5.35846996e+01 -3.25042457e+01 -2.07994772e+01 58 -2.34004925e+01 -3.34420111e+01 -3.77459016e+01 | -2.34004925e+01 -3.34420111e+01 -3.77459016e+01 59 2.38588542e+01 3.23666299e+01 3.60804011e+01 | 2.38588542e+01 3.23666299e+01 3.60804011e+01 60 -2.07778167e+00 -1.64405417e+00 -5.53728380e+00 | -2.07778167e+00 -1.64405417e+00 -5.53728380e+00 61 3.01654439e+00 4.59881503e+00 5.93110020e+00 | 3.01654439e+00 4.59881503e+00 5.93110020e+00 62 -2.87480698e+01 3.87392601e+01 2.25456908e+01 | -2.87480698e+01 3.87392601e+01 2.25456908e+01 63 2.85805635e-01 -1.45876787e+00 -8.28713043e-01 | 2.85805635e-01 -1.45876787e+00 -8.28713043e-01 ------------------------------------------------------------------------------------------------------------------------- PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------- ========================================================================================================================= To pass this verification check the model must be invariant with respect to perumutation symmetry for all configurations it was able to compute. Grade: P Comment: Model energy has permutation symmetry for all configurations the model was able to compute.